Math 13 Homework #4

Why, sometimes I've believed as many as six impossible things before breakfast.
Lewis Carroll

Quiz

Remember that we have a quiz on Monday 10/5 on Lectures 2 - 4.

Reading

Read what we will cover in the next class: 12.3.

When reading 12.3 pay special attention to the following concepts:

  • partial derivative, techniques for calculating partial derivatives, the meaning of partial derivatives, higher partial derivatives, Clairaut's Theorem, partial differential equations, the Laplace equation, the wave equation.

Problems

The following problems are due by the beginning of class on Wednesday 10/7.
  • 12.2: 3, 6, 8, 21, 31, 32, 33, 39, 44.

Maple & Web Stuff from class

The source code for today's Maple pictures can be found at:

A FINAL NOTE

On Monday we are going to start looking at partial derivatives. It might be a good idea to go back and refresh your memories of derivatives from your single-variable course. You should know how to do things like derivatives of polynomials, the trig functions, and exponentials. Also, remind yourself about things like the product rule, the quotient rule, and the chain rule.

The following is a list of derivatives which you should know how to do; i.e., calculate dy/dx for each of the following:

  • y = x^3 + tan(x)
  • y = 2(x^3) + 4
  • y = 4cos(3x)
  • y = x^2(sin(x^2))
  • y = x^3/(x^4 + 2)
  • y = e^(sinx)
  • y = x(ln(x))
Note: ^ is a bit of programming lingo and means that the following function is an exponent.